Dark Matter Substructure Research Articles

DASH: a library of dynamical subhalo evolution

The abundance and demographics of dark matter substructure is important for many areas in astrophysics and cosmological $N$-body simulations have been the primary tool used to investigate them. However, it has recently become clear that the simulations are subject to numerical artefacts, which hampers a proper treatment of the tidal evolution of subhaloes. Unfortunately, no analytical models that accurately describe subhalo evolution exist either. We therefore present a library of idealized, high resolution $N$-body simulations of the tidal evolution of individual subhaloes that can be used to calibrate semi-analytical models and to complement cosmological simulations. The simulations focus on minor mergers, i.e., the mass of the subhalo is much smaller than that of the host halo, such that the impact of dynamical friction is negligible. This setup allows the adoption of a fixed analytical potential for modelling the host halo. The dynamical evolution of subhaloes is followed with $N$-body computations. In the library, four parameters, two of which characterize the subhalo orbit with respect to the host halo, and the two concentrations of the host- and subhalo, are varied over the ranges encountered in cosmological simulations. We show several representative examples from the library that illustrate the evolution of the subhalo mass and velocity dispersion profiles. Additionally, we make publicly available a pre-trained non-parametric model of the subhalo mass evolution based on random forest regression. This model is able to interpolate the simulation data at the 0.1\,dex level and provides efficient access to the data for further use in modelling.

Effects of baryonic and dark matter substructure on the Pal 5 stream

Gravitational encounters between small-scale dark matter substructure and cold stellar streams in the Milky Way halo lead to density perturbations in the latter, making streams an effective probe for detecting dark matter substructure. The Pal 5 stream is one such system for which we have some of the best data. However, Pal 5 orbits close to the center of the Milky Way and has passed through the Galactic disk many times, where its structure can be perturbed by baryonic structures such as the Galactic bar and giant molecular clouds (GMCs). In order to understand how these baryonic structures affect Pal 5's density, we present a detailed study of the effects of the Galactic bar, spiral structure, GMCs, and globular clusters on the Pal 5 stream. We estimate the effect of each perturber on the stream density by computing its power spectrum and comparing it to the power induced by a CDM-like population of dark matter subhalos. We find that the bar and GMCs can each individually create power that is comparable to the observed power on large scales, leaving little room for dark matter substructure, while spirals are subdominant on all scales. On degree scales, the power induced by the bar is small, but GMCs create small-scale density variations that are similar in amplitude to the dark-matter induced variations but otherwise indistinguishable from it. These results demonstrate that Pal 5 is a poor system for constraining the dark matter substructure fraction and that observing streams further out in the halo will be necessary to confidently detect dark matter subhalos.

Missing Satellites Problem: Completeness Corrections to the Number of Satellite Galaxies in the MilkyWay are Consistent with Cold Dark Matter Predictions.

A critical challenge to the cold dark matter (CDM) paradigm is that there are fewer satellites observed around the MilkyWay than found in simulations of dark matter substructure. We show that there is a match between the observed satellite counts corrected by the detection efficiency of the Sloan Digital Sky Survey (for luminosities L≳340 L_{⊙}) and the number of luminous satellites predicted by CDM, assuming an empirical relation between stellar mass and halo mass. The "missing satellites problem," cast in terms of number counts, is thus solved. We also show that warm dark matter models with a thermal relic mass smaller than 4keV are in tension with satellite counts, putting pressure on the sterile neutrino interpretation of recent x-ray observations. Importantly, the total number of MilkyWay satellites depends sensitively on the spatial distribution of satellites, possibly leading to a "too many satellites" problem. Measurements of completely dark halos below 10^{8} M_{⊙}, achievable with substructure lensing and stellar stream perturbations, are the next frontier for tests of CDM.

Nature versus nurture: what regulates star formation in satellite galaxies?

We use our state-of-the-art Galaxy Evolution and Assembly (GAEA) semi-analytic model to study how and on which time-scales star formation is suppressed in satellite galaxies. Our fiducial stellar feedback model, implementing strong stellar driven outflows, reproduces relatively well the variations of passive fractions as a function of galaxy stellar mass and halo mass measured in the local Universe, as well as the `quenching' time-scales inferred from the data. We show that the same level of agreement can be obtained by using an alternative stellar feedback scheme featuring lower ejection rates at high redshift, and modifying the treatment for hot gas stripping. This scheme over-predicts the number densities of low to intermediate mass galaxies. In addition, a good agreement with the observed passive fractions can be obtained only by assuming that cooling can continue on satellites, at the rate predicted considering halo properties at infall, even after their parent dark matter substructure is stripped below the resolution of the simulation. For our fiducial model, the better agreement with the observed passive fractions can be ascribed to: (i) a larger cold gas fraction of satellites at the time of accretion, and (ii) a lower rate of gas reheating by supernovae explosions and stellar winds with respect to previous versions of our model. Our results suggest that the abundance of passive galaxies with stellar mass larger than ~10^10 Msun is primarily determined by the self-regulation between star formation and stellar feedback, with environmental processes playing a more marginal role.

Anomalies in Time Delays of Lensed Gravitational Waves and Dark Matter Substructures

Abstract Cold dark matter scenarios of hierarchical large-scale structure formation predict the existence of abundant subhalos around large galaxies. However, the number of observed dwarf galaxies is far from this theoretical prediction, suggesting that most of the subhalos could be dark or quite faint. Gravitational lensing is a powerful tool to probe the mass distribution directly irrespective of whether it is visible or dark. Time delay anomalies in strongly lensed quasar systems are complementary to flux-ratio anomalies in probing dark matter substructure in galaxies. Here we propose that lensed gravitational waves detected by the third-generation ground detectors with quite accurate time delay measurements could be a much better tool for this study than conventional techniques. Combined with good quality images of lensed host galaxies identified by the electromagnetic counterpart measurements, lensed gravitational wave signals could make the systematic errors caused by dark matter substructures detectable at levels of several percent, depending on their mass functions, internal distribution of subhalos, and lensing system configuration.

Off the Beaten Path: Gaia Reveals GD-1 Stars outside of the Main Stream

Abstract Tidally disrupted globular clusters are transformed into thin, dynamically cold streams of stars that are extremely valuable tracers of the large- and small-scale distribution of mass in the Galaxy. Using data from the Gaia second data release combined with Pan-STARRS photometry, we present a sample of highly probable members of the longest cold stream in the Milky Way, GD-1. The resulting map of GD-1: (1) extends the apparent length of the stream by 20°, (2) reveals plausible locations for the progenitor, (3) detects high-contrast gaps along the stream, and (4) indicates the existence of stream members perturbed off the main stream track. These discoveries are only possible because of the exquisite astrometry from Gaia, which permits a clean separation of the stream from Milky Way stars. The additional length and a proper treatment of the progenitor will aid in dynamical modeling of GD-1 for mapping the large-scale dark matter distribution. The complex morphology of the stream points to a turbulent history; detailed phase-space properties of the perturbed stream members could potentially constrain dark matter substructure in the Milky Way.

Cold Filamentary Accretion and the Formation of Metal-poor Globular Clusters and Halo Stars

Abstract We propose that cold filamentary accretion in massive galaxies at high redshifts can lead to the formation of star-forming clumps in the halos of these galaxies without dark matter substructure. In certain cases, these clumps can be the birthplaces of metal-poor globular clusters (MP GCs). Using cosmological simulations, we show that narrow streams of dense gas feeding massive galaxies from the cosmic web can fragment, producing star-forming clumps. We then derive an analytical model for the properties of streams as a function of halo mass and redshift, and assess when these are gravitationally unstable, when this can lead to collapse and star formation in the halo, and when it may result in the formation of MP GCs. For stream metallicities ≳ 0.01 Z ⊙ , this is likely to occur at z > 4.5 . At z ∼ 6 , the collapsing clouds have masses of ∼ ( 5 – 10 ) × 10 7 M ⊙ , and the average stream pressure is ∼ 10 6 cm − 3 K . The conditions for GC formation are met in the extremely turbulent “eyewall” at ∼ 0.3 R v , where counter-rotating streams can collide, driving very large densities. Our scenario can account for the observed kinematics and spatial distribution of MP GCs, the correlation between their mass and metallicity, and the mass ratio between the GC system and the host halo. For MW-mass halos, we infer that ∼ 30 % of MP GCs could have formed in this way, with the remainder likely accreted in mergers. Our predictions for GC formation along circumgalactic filaments at high redshift are testable with JWST.

Probing the nature of dark matter particles with stellar streams

A key prediction of the standard cosmological model—which relies on the assumption that dark matter is cold, i.e. non-relativistic at the epoch of structure formation—is the existence of a large number of dark matter substructures on sub-galactic scales. This assumption can be tested by studying the perturbations induced by dark matter substructures on cold stellar streams. Here, we study the prospects for discriminating cold from warm dark matter by generating mock data for upcoming astronomical surveys such as the Large Synoptic Survey Telescope (LSST), and reconstructing the properties of the dark matter particle from the perturbations induced on the stellar density profile of a stream. We discuss the statistical and systematic uncertainties, and show that the method should allow to set stringent constraints on the mass of thermal dark matter relics, and possibly to yield an actual measurement of the dark matter particle mass if it is in the \U0001d4aa(1) keV range.

Dark matter substructure cannot explain properties of the Fermi Galactic Centre excess

An excess of gamma rays has been identified at the centre of the Milky Way, and annihilation of dark matter has been posited as a potential source. This hypothesis faces significant challenges: difficulty characterizing astrophysical backgrounds, the need for a non-trivial adiabatic contraction of the inner part of the Milky Way's dark matter halo, and recent observations of photon clustering, which suggest that the majority of the excess is due to unresolved point sources. Here we point out that the apparent point-like nature of the emission rules out the dark matter interpretation of the excess entirely. Attempting to model the emission with dark matter point sources either worsens the problem with the inner slope, requires an unrealistically large minihalo fraction toward the Galactic Centre, or overproduces the observed emission at higher latitudes.

Revealing the dark matter halo with axion direct detection

The next generation of axion direct detection experiments may rule out or confirm axions as the dominant source of dark matter. We develop a general likelihood-based framework for studying the time-series data at such experiments, with a focus on the role of dark-matter astrophysics, to search for signatures of the QCD axion or axion like particles. We illustrate how in the event of a detection the likelihood framework may be used to extract measures of the local dark matter phase-space distribution, accounting for effects such as annual modulation and gravitational focusing, which is the perturbation to the dark matter phase-space distribution by the gravitational field of the Sun. Moreover, we show how potential dark matter substructure, such as cold dark matter streams or a thick dark disk, could impact the signal. For example, we find that when the bulk dark matter halo is detected at 5$\sigma$ global significance, the unique time-dependent features imprinted by the dark matter component of the Sagittarius stream, even if only a few percent of the local dark matter density, may be detectable at $\sim$2$\sigma$ significance. A co-rotating dark disk, with lag speed $\sim$50 km$/$s, that is $\sim$20$\%$ of the local DM density could dominate the signal, while colder but as-of-yet unknown substructure may be even more important. Our likelihood formalism, and the results derived with it, are generally applicable to any time-series based approach to axion direct detection.

Modeling evolution of dark matter substructure and annihilation boost

We study evolution of dark matter substructures, especially how they lose the mass and change density profile after they fall in gravitational potential of larger host halos. We develop an analytical prescription that models the subhalo mass evolution and calibrate it to results of N-body numerical simulations of various scales from very small (Earth size) to large (galaxies to clusters) halos. We then combine the results with halo accretion histories, and calculate the subhalo mass function that is physically motivated down to Earth-mass scales. Our results --- valid for arbitrary host masses and redshifts --- show reasonable agreement with those of numerical simulations at resolved scales. Our analytical model also enables self-consistent calculations of the boost factor of dark matter annhilation, which we find to increase from tens of percent at the smallest (Earth) and intermediate (dwarfs) masses to a factor of several at galaxy size, and to become as large as a factor of $\sim$10 for the largest halos (clusters) at small redshifts. Our analytical approach can accommodate substructures in the subhalos (sub-subhalos) in a consistent framework, which we find to give up to a factor of a few enhancement to the annihilation boost. Presence of the subhalos enhances the intensity of the isotropic gamma-ray background by a factor of a few, and as the result, the measurement by Fermi Large Area Telescope excludes the annihilation cross section greater than $\sim$$4\times 10^{-26}$ cm$^3$ s$^{-1}$ for dark matter masses up to $\sim$200 GeV.

The metal-poor stellar halo in RAVE-TGAS and its implications for the velocity distribution of dark matter

The local velocity distribution of dark matter plays an integral role in interpreting the results from direct detection experiments. We previously showed that metal-poor halo stars serve as excellent tracers of the virialized dark matter velocity distribution using a high-resolution hydrodynamic simulation of a Milky Way-like halo. In this paper, we take advantage of the first Gaia data release, coupled with spectroscopic measurements from the RAdial Velocity Experiment (RAVE), to study the kinematics of stars belonging to the metal-poor halo within an average distance of ∼5 kpc of the Sun. We study stars with iron abundances [Fe/H] < −1.5 and −1.8 that are located more than 1.5 kpc from the Galactic plane. Using a Gaussian mixture model analysis, we identify the stars that belong to the halo population, as well as some kinematic outliers. We find that both metallicity samples have similar velocity distributions for the halo component, within uncertainties. Assuming that the stellar halo velocities adequately trace the virialized dark matter, we study the implications for direct detection experiments. The Standard Halo Model, which is typically assumed for dark matter, is discrepant with the empirical distribution by ∼6σ, predicts fewer high-speed particles, and is anisotropic. As a result, the Standard Halo Model overpredicts the nuclear scattering rate for dark matter masses below ∼10 GeV. The kinematic outliers that we identify may potentially be correlated with dark matter substructure, though further study is needed to establish this correspondence.

The BOSS Emission-line Lens Survey. V. Morphology and Substructure of Lensed Lyα Emitters at Redshift Z ≈ 2.5 in the BELLS GALLERY

Abstract We present a morphological study of the 17 lensed Lyα emitter (LAE) galaxies of the Baryon Oscillation Spectroscopic Survey Emission-Line Lens Survey (BELLS) for the GALaxy-Lyα EmitteR sYstems (BELLS GALLERY) sample. This analysis combines the magnification effect of strong galaxy–galaxy lensing with the high resolution of the Hubble Space Telescope to achieve a physical resolution of ∼80 pc for this 2 &lt; z &lt; 3 LAE sample, allowing a detailed characterization of the LAE rest-frame ultraviolet continuum surface brightness profiles and substructure. We use lens-model reconstructions of the LAEs to identify and model individual clumps, which we subsequently use to constrain the parameters of a generative statistical model of the LAE population. Since the BELLS GALLERY sample is selected primarily on the basis of Lyα emission, the LAEs that we study here are likely to be directly comparable to those selected in wide-field, narrowband LAE surveys, in contrast with the lensed LAEs identified in cluster-lensing fields. We find an LAE clumpiness fraction of approximately 88%, which is significantly higher than that found in previous (non-lensing) studies. We find a well-resolved characteristic clump half-light radii of ∼350 pc, a scale comparable to the largest H ii regions seen in the local universe. This statistical characterization of LAE surface-brightness profiles will be incorporated into future lensing analyses using the BELLS GALLERY sample to constrain the incidence of dark-matter substructure in the foreground lensing galaxies.

Dark matter substructure in numerical simulations: a tale of discreteness noise, runaway instabilities, and artificial disruption

To gain understanding of the complicated, non-linear and numerical processes associated with the tidal evolution of dark matter subhaloes in numerical simulation, we perform a large suite of idealized simulations that follow individual N-body subhaloes in a fixed, analytical host halo potential. By varying both physical and numerical parameters, we investigate under what conditions the subhaloes undergo disruption. We confirm the conclusions from our more analytical assessment in van den Bosch et al. that most disruption is numerical in origin; as long as a subhalo is resolved with sufficient mass and force resolution, a bound remnant survives. This implies that state-of-the-art cosmological simulations still suffer from significant overmerging. We demonstrate that this is mainly due to inadequate force-softening, which causes excessive mass loss and artificial tidal disruption. In addition, we show that subhaloes in N-body simulations are susceptible to a runaway instability triggered by the amplification of discreteness noise in the presence of a tidal field. These two processes conspire to put serious limitations on the reliability of dark matter substructure in state-of-the-art cosmological simulations. We present two criteria that can be used to assess whether individual subhaloes in cosmological simulations are reliable or not, and advocate that subhaloes that satisfy either of these two criteria be discarded from further analysis. We discuss the potential implications of this work for several areas in astrophysics.

Flux-ratio anomalies from discs and other baryonic structures in the Illustris simulation

The flux ratios in the multiple images of gravitationally lensed quasars can provide evidence for dark matter substructure in the halo of the lensing galaxy if the flux ratios differ from those predicted by a smooth model of the lensing galaxy mass distribution. However, it is also possible that baryonic structures in the lensing galaxy, such as edge-on discs, can produce flux-ratio anomalies. In this work, we present the first statistical analysis of flux-ratio anomalies due to baryons from a numerical simulation perspective. We select galaxies with various morphological types in the Illustris simulation and ray-trace through the simulated halos, which include baryons in the main lensing galaxies but exclude any substructures, in order to explore the pure baryonic effects. Our ray-tracing results show that the baryonic components can be a major contribution to the flux-ratio anomalies in lensed quasars and that edge-on disc lenses induce the strongest anomalies. We find that the baryonic components increase the probability of finding high flux-ratio anomalies in the early-type lenses by about 8% and by about 10 - 20% in the disc lenses. The baryonic effects also induce astrometric anomalies in 13% of the mock lenses. Our results indicate that the morphology of the lens galaxy becomes important in the analysis of flux-ratio anomalies when considering the effect of baryons, and that the presence of baryons may also partially explain the discrepancy between the observed (high) anomaly frequency and what is expected due to the presence of subhalos as predicted by the CDM simulations.

Power spectrum of dark matter substructure in strong gravitational lenses

Studying the smallest self-bound dark matter structure in our Universe can yield important clues about the fundamental particle nature of dark matter. Galaxy-scale strong gravitational lensing provides a unique way to detect and characterize dark matter substructures at cosmological distances from the Milky Way. Within the cold dark matter (CDM) paradigm, the number of low-mass subhalos within lens galaxies is expected to be large, implying that their contribution to the lensing convergence field is approximately Gaussian and could thus be described by their power spectrum. We develop here a general formalism to compute from first principles the substructure convergence power spectrum for different populations of dark matter subhalos. As an example, we apply our framework to two distinct subhalo populations: a truncated Navarro-Frenk-White subhalo population motivated by standard CDM, and a truncated cored subhalo population motivated by self-interacting dark matter (SIDM). We study in detail how the subhalo abundance, mass function, internal density profile, and concentration affect the amplitude and shape of the substructure power spectrum. We determine that the power spectrum is mostly sensitive to a specific combination of the subhalo abundance and moments of the mass function, as well as to the average tidal truncation scale of the largest subhalos included in the analysis. Interestingly, we show that the asymptotic slope of the substructure power spectrum at large wave number reflects the internal density profile of the subhalos. In particular, the SIDM power spectrum exhibits a characteristic steepening at large wave number absent in the CDM power spectrum, opening the possibility of using this observable, if at all measurable, to discern between these two scenarios.

Disruption of dark matter substructure: fact or fiction?

Accurately predicting the demographics of dark matter (DM) substructure is of paramount importance for many fields of astrophysics, including gravitational lensing, galaxy evolution, halo occupation modeling, and constraining the nature of dark matter. Because of its strongly non-linear nature, DM substructure is typically modeled using N-body simulations, which reveal that large fractions of DM subhaloes undergo complete disruption. In this paper we use both analytical estimates and idealized numerical simulations to investigate whether this disruption is mainly physical, due to tidal heating and stripping, or numerical (i.e., artificial). We show that, contrary to naive expectation, subhaloes that experience a tidal shock $\Delta E$ that exceeds the subhalo's binding energy, $|E_{\rm b}|$, do not undergo disruption, even when $\Delta E/|E_{\rm b}|$ is as large as 100. Along the same line, and contrary to existing claims in the literature, instantaneously stripping matter from the outskirts of a DM subhalo also does not result in its complete disruption, even when the instantaneous remnant has positive binding energy. In addition, we show that tidal heating due to high-speed (impulsive) encounters with other subhaloes (`harassment'), is negligible compared to the tidal effects due to the host halo. Hence, we conclude that, in the absence of baryonic processes, the complete, physical disruption of CDM substructure is extremely rare, and that most disruption in numerical simulations therefore must be artificial. We discuss various processes that have been associated with numerical overmerging, and conclude that inadequate force-softening is the most likely culprit.

A Robust Mass Estimator for Dark Matter Subhalo Perturbations in Strong Gravitational Lenses

Abstract A few dark matter substructures have recently been detected in strong gravitational lenses through their perturbations of highly magnified images. We derive a characteristic scale for lensing perturbations and show that they are significantly larger than the perturber’s Einstein radius. We show that the perturber’s projected mass enclosed within this radius, scaled by the log-slope of the host galaxy’s density profile, can be robustly inferred even if the inferred density profile and tidal radius of the perturber are biased. We demonstrate the validity of our analytic derivation using several gravitational lens simulations where the tidal radii and the inner log-slopes of the density profile of the perturbing subhalo are allowed to vary. By modeling these simulated data, we find that our mass estimator, which we call the effective subhalo lensing mass, is accurate to within about 10% or smaller in each case, whereas the inferred total subhalo mass can potentially be biased by nearly an order of magnitude. We therefore recommend that the effective subhalo lensing mass be reported in future lensing reconstructions, as this will allow for a more accurate comparison with the results of dark matter simulations.

Statistics of dark matter substructure – III. Halo-to-halo variance

We present a study of unprecedented statistical power regarding the halo-to-halo variance of dark matter substructure. Using a combination of N-body simulations and a semi-analytical model, we investigate the variance in subhalo mass fractions and subhalo occupation numbers, with an emphasis on how these statistics scale with halo formation time. We demonstrate that the subhalo mass fraction, f_sub, is mainly a function of halo formation time, with earlier forming haloes having less substructure. At fixed formation redshift, the average f_sub is virtually independent of halo mass, and the mass dependence of f_sub is therefore mainly a manifestation of more massive haloes assembling later. We compare observational constraints on f_sub from gravitational lensing to our model predictions and simulation results. Although the inferred f_sub are substantially higher than the median LCDM predictions, they fall within the 95th percentile due to halo-to-halo variance. We show that while the halo occupation distribution of subhaloes, P(N|M), is super-Poissonian for large <N>, a well established result, it becomes sub-Poissonian for <N> < 2. Ignoring the non-Poissonity results in systematic errors of the clustering of galaxies of a few percent, and with a complicated scale- and luminosity-dependence. Earlier-formed haloes have P(N|M) closer to a Poisson distribution, suggesting that the dynamical evolution of subhaloes drives the statistics towards Poissonian. Contrary to a recent claim, the non-Poissonity of subhalo occupation statistics does not vanish by selecting haloes with fixed mass and fixed formation redshift. Finally, we use subhalo occupation statistics to put loose constraints on the mass and formation redshift of the Milky Way halo. Using observational constraints on the V_max of the most massive satellites, we infer that 0.25<M_vir/10^12M_sun/h<1.4 and 0.1<z_f<1.4 at 90% confidence.

Discovery of the First Quadruple Gravitationally Lensed Quasar Candidate with Pan-STARRS

Abstract We report the serendipitous discovery of the first gravitationally lensed quasar candidate from Pan-STARRS. The grizy images reveal four point-like images with magnitudes between 14.9 and 18.1 mag. The colors of the point sources are similar, and they are more consistent with quasars than with stars or galaxies. The lensing galaxy is detected in the izy bands, with an inferred photometric redshift of ∼0.6, lower than that of the point sources. We successfully model the system with a singular isothermal ellipsoid with shear, using the relative positions of the five objects as constraints. While the brightness ranking of the point sources is consistent with that of the model, we find discrepancies between the model-predicted and observed fluxes, likely due to microlensing by stars and millilensing due to the dark matter substructure. In order to fully confirm the gravitational lens nature of this system and add it to the small but growing number of the powerful probes of cosmology and astrophysics represented by quadruply lensed quasars, we require further spectroscopy and high-resolution imaging.